John asks his friend, Paul, to borrow some money to make it to payday. Paul woul

Question

John asks his friend, Paul, to borrow some money to make it to payday. Paul would like to help John, but John is known for not paying his debts. At the same time Paul is making his decision, John is deciding whether to buy lottery tickets. He really likes the lottery. If he buys them, he will not be able to pay Paul back.

If Paul decides not to loan John the money, Paul gets 0. If John then buys lottery tickets, he gets 0. If he decides not to buy lottery tickets, he gets -1. If Paul decides to loan John the money and John plays the lottery, Paul gets -2 and John gets 8. If Paul decides to loan John the money and John does not play the lottery, Paul gets 3 and John gets 6. If this game is played just once, determine the equilibrium. What is John’s expected payoff?

Paul talks to John about making this a repetitive offer. It turns out that John has some rich relatives who might help him out regardless of what happens in the previous games. John has a 70% chance of becoming independently wealthy after each round and never returning to ask for a loan. Considering all of this new information, what is John’s decision now? What is his expected payoff?

Finally, a benevolent aunt feels sorry for her family. Any time John is denied a loan by a friend, she gives him some worth 2, bringing his payoff up to 1 if he does not play the lottery and 2 if he does. Now what is John’s decision? What is his payoff? (Note: we are still working off of the discount factor for a repetitive offer)

In which of these three scenarios is John the best off?

Explanation / Answer

Formulating the game matrix:

Among all the stages the common is :

Paul Does not Loan and John Plays Lottery

The outcome of the equillibrium is (0,0) for Paul and John.

So now the Skew is on John Lottery, as No matter what he will go for Lottery and So in such a case the best option for Paul is not to loan.

So The payoff is 0,0 for Paul and John.

Whan aunt is in the picture: The game outcomes are as below,

So again doing the startegy we get the equillibrium is the same

Paul Does not Loan and John Plays Lottery

But the outcome are: 0 for Paul and 2 for John.

So out of the three the last one is the best for John and all the ones are same for Paul.

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.